First and second orders temperature-compensated resonator

ABSTRACT

A temperature-compensated resonator includes a body used in deformation, wherein the core ( 58, 58′, 18 ) of the body ( 3, 5, 7, 15, 23, 25, 27, 33, 35, 37, 43, 45, 47 ) is formed from a plate formed at a cut angle (θ′) in a quartz crystal determining the first and second orders temperature coefficients (α, β, α′, β′). According to the invention, the body ( 3, 5, 7, 15, 23, 25, 27, 33, 35, 37, 43, 45, 47 ) includes a coating ( 52, 54, 56, 52′, 54′, 56′, 16 ) deposited at least partially on the core ( 58, 58′, 18 ) and having first and second orders Young&#39;s modulus variations (CTE 1 , CTE 2 , CTE 1 ′, CTE 2 ′) according to temperature of opposite signs respectively to the first and second orders temperature coefficients (α, β, α′, β′) of the resonator so as to render compensated first and second orders temperature coefficients substantially zero.

This application claims priority from European Patent Application No.10165563.7 filed Jun. 10, 2010, the entire disclosure of which isincorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to a temperature-compensated resonator of thesprung balance, tuning fork or more generally MEMS type formanufacturing a time base or frequency whose first and second ordertemperature coefficients are substantially zero.

BACKGROUND OF THE INVENTION

EP Patent No. 1 422 436 discloses a balance spring or a hairspringformed of silicon and coated with silicon dioxide so as to make thetemperature coefficient substantially zero around COSC (ContrôleOfficiel Suisse des Chronomètres) certification process temperatures,i.e. between +8 and +38° C. Likewise, WO 2008-043727 document disclosesa MEMS resonator which has similar properties of low drift from itsYoung's modulus within the same temperature range.

However, even only the second order frequency drift in the abovedisclosures can require complex corrections depending upon theapplication. For example, for electronic quartz watches to be able to beCOSC certified, an electronic correction has to be carried out based ona temperature measurement.

SUMMARY OF THE INVENTION

It is an object of the present invention to overcome all or part of theaforementioned drawbacks, by providing a first and second ordertemperature-compensated quartz resonator.

The invention therefore relates to a temperature-compensated resonatorincluding a body used in deformation, the core of the body being formedfrom a plate formed at a cut angle (θ) in a quartz crystal thatdetermines the first and second order temperature coefficients,characterized in that the body includes a coating, which is at leastpartially deposited on the core and has first and second ordertemperature dependent variations of the Young's modulus of oppositesigns respectively to said first and second order temperaturecoefficients of said resonator so that the latter are renderedsubstantially zero.

Advantageously according to the invention, the resonator body used indeformation has only one coating to compensate for two orders. Thus,depending upon the size and sign of each order of the coating material,the cut angle in the single crystal quartz and the thickness of thecoating are calculated so as to compensate for the first two orders.

In accordance with other advantageous features of the invention:

-   -   the body includes a substantially quadrilateral-shaped section        whose faces are in identical pairs;    -   the body includes a substantially quadrilateral-shaped section        whose faces are entirely coated;    -   the cut angle of the plate is selected so that said first and        second order temperature coefficients are negative and the        coating includes positive first and second order Young's modulus        variations;    -   the coating includes germanium dioxide;    -   the cut angle of the plate is selected so that said first and        second order temperature coefficients are respectively positive        and negative and the coating has first and second order Young's        modulus variations which are respectively negative and positive;    -   the coating includes synthetic diamond;    -   the body is a bar wound around itself to form a balance spring        or a hairspring and is coupled with an inertia block;    -   the body includes at least two symmetrically mounted arms        forming a tuning fork;    -   the tuning fork is of the inverted type and/or grooved type        and/or conical type and/or flipper type;    -   the body is a MEMS (Micro-Electro-Mechanical System).

Finally, the invention also relates to a time or frequency base, suchas, for example a timepiece, characterized in that it includes at leastone resonator according to any of the preceding variants.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages will appear clearly from the followingdescription, given by way of non-limiting indication, with reference tothe annexed drawings, in which:

FIGS. 1 to 4 are general perspective diagrams of several types of tuningfork resonators;

FIGS. 5A, 5B, 6A and 6B are alternatives of the resonator sections ofFIGS. 1 to 4;

FIG. 7 is a general perspective view of one part of a sprung balanceresonator;

FIG. 8 is a representative section of the balance spring of FIG. 7;

FIG. 9 is a graph showing the first and second order temperaturecoefficients of a tuning fork according the cut angle thereof in asingle crystal quartz;

FIG. 10 is a graph showing the first and second order temperaturecoefficient variations of a quartz tuning fork cut at an angle equal to−8.4° relative to the Z axis according to the thickness of a layer ofgermanium dioxide;

FIGS. 11 and 12 are schematic diagrams of a cut angle relative to thecrystallographic axes of a quartz crystal.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

As explained above, the invention relates to a quartz resonator whichmay be of the sprung balance or tuning fork type or more generally aMEMS (Micro-Electro-Mechanical System). To simplify explanation of theinvention, the only applications presented below are to a sprung balanceand tuning forks. However, those skilled in the art could accomplishother resonator applications without any difficulty from the teachingbelow.

The graph of FIG. 9 shows the characterization of the first and secondorder temperature coefficient drift for current tuning fork resonatorsaccording to the cut angle along the z axis of a quartz crystal.

FIGS. 11 and 12 show the spatial interpretation of the z axis relativeto a single crystal quartz. A quartz crystal has crystallographic axesx, y, z. The x axis is the electrical axis and the y axis is themechanical axis. In the example of FIGS. 11 and 12, the height h of thebalance spring or tuning fork thus has an orientation relative tocrystallographic axis z which depends upon the cut angle θ that has beenchosen.

Of course, cut angle θ will not be limited to a single angle relative toan axis, since rotations at several angles relative to several axes arealso possible to obtain the desired technical effect within the presentinvention. By way of example, the final cut angle θ could thus be theresult of a first angle φ relative to the x axis and a second angle ⊖relative to the z axis.

FIG. 9 shows, as illustrated in a continuous line, that the first ordertemperature coefficient α intersects the zero axis at around a cut angleof 0 degree and 12 degrees. It is thus clear that, depending upon thecut angle of the single crystal quartz, it is possible to “naturally”obtain a first order temperature coefficient α that is substantiallyzero, i.e. the resonator has a first order frequency variation that isvirtually independent of temperature.

These advantageous features have been used for several decades to formtime bases for timepieces with a cut angle of close to 0 degree.

FIG. 9 also shows, as illustrated in dotted lines, that the second ordertemperature coefficient β never intersects the zero axis. Hence, it isclear that even with the current cut angle close to 0 degrees, thequartz remains sensitive to temperature variations because of variationin the second order temperature coefficient β, but to a lesser degreethan with the first order temperature coefficient α.

Finally, in FIG. 9 it can be seen that the negative cut angles in thesingle crystal quartz systematically form a resonator whose first α andsecond β orders temperature coefficients are negative.

Advantageously, the idea of the invention is to adapt a quartz cut angleθ with a single layer of coating in order to compensate for the first αand second β orders temperature coefficients of quartz resonators toobtain a resonator that is insensitive to temperature variations.

By way of definition, the relative frequency variation of a resonatorfollows the relationship below:

$\frac{\Delta\; f}{f_{0}} = {A + {\alpha \cdot \left( {T - T_{0}} \right)} + {\beta \cdot \left( {T - T_{0}} \right)^{2}} + {\gamma \cdot \left( {T - T_{0}} \right)^{3}}}$where:

$- \frac{\Delta\; f}{f_{0}}$is the relative frequency variation, expressed in ppm (10⁻⁶);

-   -   A is a constant which depends upon the point of reference, in        ppm;    -   T₀ is the reference temperature, in ° C.;    -   α is the first order temperature coefficient, expressed in ppm.°        C.⁻¹;    -   β is the second order temperature coefficient expressed in ppm.°        C.⁻²;    -   γ is the third order temperature coefficient, expressed in ppm.°        C.⁻³.

Moreover, the thermo-elastical coefficient (CTE) represents the relativevariation of the Young's modulus according to temperature. The terms “α”and “β” which are used below thus respectively represent the first andsecond order temperature coefficients, i.e. the relative frequencyvariation of the resonator according to temperature. The terms “α” and“β” depend upon the thermo-elastical coefficient of the resonator bodyand the coefficients of thermal expansion of the body. Moreover, theterms “α” and “β” also take into account the coefficients peculiar toany separate inertia member, such as, for example, the balance for asprung-balance resonator.

As the oscillations of any resonator intended for a time or frequencybase have to be maintained, thermal dependence may also include acontribution from the maintenance system. Preferably, the resonator bodyis a quartz core coated with a single coating on at least one part orthe whole of the external surface thereof, and possibly, on top of themetallizations usually necessary if piezoelectric actuation is desired.Evidently, in this latter case, whichever coating is chosen, theconnecting pads must remain free.

The examples illustrated in FIGS. 1 to 4 show tuning fork variants 1,21, 31, 41 applicable to the invention. They are formed of a base 3, 23,33, 43 connected to two arms 5, 7, 25, 27, 35, 37, 45, 47 which areintended to oscillate in respective directions B and C.

The variants of FIGS. 2 to 4 show inverted type tuning forks 21, 31, 41,i.e. base 23, 33, 43 is extended between the two arms 25, 27, 35, 37,45, 47 so as to optimise the uncoupling between the fastening and theactive area of the resonator 21, 31, 41 and optimise the length of thevibrating arms for a given surface of matter. The variants of FIGS. 2 to4 show grooved type tuning forks 21, 31, 41, i.e. the two arms 25, 27,35, 37, 45, 47 include grooves 24, 26, 34, 36, 44, 46 for the depositionof electrodes to increase the piezoelectric coupling and thereby provideresonators of small size with excellent electrical parameters.

Moreover, FIG. 1 shows a conical arm variant 5, 7, i.e. wherein thesection gradually decreases away from base 3 so as to distribute theelastic stresses better over the length of the arms and thereby increasethe coupling of the electrodes. Finally, FIGS. 1 and 4 show flipper typetuning forks, 1, 41, i.e. both arms 5, 7, 45, 47 include flippes 2, 8,42, 48 at the end thereof to increase the oscillation inertia of arms 5,7, 45, 47 of resonator 1, 41, to provide resonators with optimisedlength for a given frequency. It is thus clear that there is a multitudeof possible tuning fork variants which may, in a non exhaustive manner,be of the inverted and/or grooved and/or conical and/or flipper type.

Advantageously according to the invention, each tuning fork 1, 21, 31,41 includes first α and second β orders temperature coefficients whichare compensated for by the deposition of a layer 52, 54, 56, 52′, 54′,56′ on core 58, 58′ of tuning fork 1, 21, 31, 41. FIGS. 5A, 5B, 6A and6B propose four non-exhaustive cross-section examples of tuning forks 1,21, 31, 41 along plane A-A which show more clearly the quadrilateral orH-shaped section thereof at least partially coated with a layer 52, 54,56, 52′, 54′, 56′. Of course, coatings 52, 54, 56, 52′, 54′, 56′ are notto scale relative to the dimensions of core 58, 58′, in order to showmore clearly the location of each part 52, 54, 56, 52′, 54′, 56′.

The study was first carried out for a tuning fork resonator 1 cut in asingle crystal quartz along negative angles relative to the z axis, i.e.along negative first α and second β orders temperature coefficients.Materials with positive first and second orders thermo-elasticalcoefficients CTE1, CTE2 were thus sought. It was discovered thatgermanium oxide (GeO₂), tantalum oxide (Ta₂O₅) and stabilised zirconiumor hafnium oxides respond to these features.

Analyses were carried out to find a cut angle θ in the quartz with asingle layer of coating in order to compensate for the first α andsecond β order temperature coefficients of quartz resonators. For thecase of FIG. 5A, i.e. a coating 52, 54 on each flank of arm 5, 7 oftuning fork 1, the first α and second β orders temperature coefficientsof tuning fork resonator 1 were found to converge at an angle θ of−8.408 degrees relative to the z axis and a thickness d of 5.47 μm foreach layer 2, 4.

This convergence is illustrated in FIG. 10 which clearly shows that thefirst α and second β orders temperature coefficients of tuning fork 1both intersect the zero axis for a same thickness d of layers 2, 4.

For FIG. 6A, i.e. a coating 56 that completely covers arms 5, 7 oftuning fork 1, the first α and second β orders temperature coefficientsof tuning fork resonator 1 were found to converge at an angle θ of−8.416 degrees relative to the z axis and a thickness d of 4.26 μm forlayer 6. It is thus concluded that cut angle θ is substantiallyequivalent to the variant of FIG. 5A, however the necessary thickness dof coating 56 is much smaller.

In a similar interpretation for grooved tuning fork sections illustratedin FIGS. 5B and 6B, an angle θ and a thickness d can also be determined.The case of FIG. 6B is particularly advantageous in that coating 56′ atthe edges of the grooves increases the surface on which the compensationlayer is active. It is thus clear, for the particular case of FIG. 6B,that the thickness d of coating 56′ will necessarily be even smaller.

It is to be noted that, for all of the above variants, although arms 5,7, 25, 27, 35, 37, 45, 47 are necessarily coated, base 3, 23, 33, 43does not necessarily have to be. Indeed, it is at the areas of stressthat coating 52, 54, 56, 52′, 54′, 56′ has to be present.

In the example illustrated in FIGS. 7 and 8, a balance spring 11 can beseen whose body 15 is integral with the collet 13 and wherein the firstα and second β orders temperature coefficients of the body arecompensated. FIG. 8 proposes a cross-section of body 15 of balancespring 11 that shows more clearly the quadrilateral-shaped sectionthereof. Body 15 can thus be defined by the length l, height h andthickness e thereof. FIG. 8 shows an example where core 18 is entirelycoated in a similar manner to FIG. 6A. Of course, FIG. 8 only shows anon-limiting example and, as for tuning forks 1, 21, 31, 41, balancespring 11 may have a coating over at least one part or the entireexternal surface of body 15.

The study was thus carried out secondly for a sprung balance resonatorwhose balance spring 11 is cut into a single crystal quartz withnegative first α and second β orders temperature coefficients and withcoating materials whose first and second orders thermo-elasticalcoefficients CTE1, CTE2 are positive.

Analyses were carried out to find a cut angle θ in the quartz with asingle layer of coating in order to compensate for the first α andsecond β orders temperature coefficients of quartz resonators.

For the case of FIG. 8, i.e. a coating 16 that totally covers body 15 ofbalance spring 11, the first α and second β orders temperaturecoefficients of the resonator were found to converge for several thermalexpansion values of the balance:

α_(bal) θ d 5 −15.9 8.5 10 −12.3 7.2 15 −8.0 6.1 20 −2.4 5.5where:

-   -   α_(bal) is the thermal expansion coefficient of the balance        expressed in ppm.° C.⁻¹;    -   θ is the cut angle in the quartz, expressed in degrees;    -   d is the thickness of the GeO₂ coating expressed in μm.

Consequently, in light of the above explanations, the teaching of theinvention is not limited to a particular coating material, or to aparticular resonator or even to a particular deposition area of thecoating. The example cut relative to the z axis of the quartz crystal isnot limiting either. Other references in the quartz crystal such as thex and y axes are also possible, just as several rotations are possible,as explained above.

It is thus clear that according to the invention it is possible, in anadvantageous manner, to compensate for the first α and second β orderstemperature coefficients of any quartz resonator with a single layerwhose first and second orders thermo-elastical coefficients CTE1, CTE2are of opposite signs to α and β. It must thus be understood that it isalso possible to compensate for the alternative cuts θ′ in a singlecrystal quartz wherein the first α and second β orders temperaturecoefficients are not negative.

By way of non-limiting example, if alternative first and second orderstemperature coefficients α′ and β′ are respectively positive andnegative, it is possible to use an alternative coating whose first andsecond orders thermo-elastical coefficients CTE1′, CTE2′ have oppositesigns, i.e. respectively negative and positive. This coating may thus beformed from a synthetic diamond which advantageously means that theresonator can be left transparent.

What is claimed is:
 1. A temperature-compensated resonator including abody used in deformation, wherein a core of the body is formed from aplate formed at a cut angle in a quartz crystal in order to determinefirst and second orders temperature coefficients that are respectivelypositive and negative, wherein the body includes a coating deposited atleast partially on the core and having first and second orders Young'smodulus variations according to temperature that are respectivelynegative and positive in order to render the first and second orderstemperature coefficients of the resonator substantially zero.
 2. Thetemperature-compensated resonator according to claim 1, wherein the bodyhas a substantially quadrilateral-shaped section with faces in identicalpairs.
 3. The temperature-compensated resonator according to claim 1,wherein the body includes a substantially quadrilateral-shaped sectionwhose faces are entirely coated.
 4. The temperature-compensatedresonator according to claim 1, wherein the coating includes syntheticdiamond.
 5. The temperature-compensated resonator according to claim 1,wherein the body is a bar wound around itself to form a balance springand is coupled with an inertia member.
 6. The temperature-compensatedresonator according to claim 1, wherein the body includes at least twosymmetrically mounted arms forming a tuning fork.
 7. Thetemperature-compensated resonator according to claim 6, wherein thetuning fork is selected from the group consisting of an inverted type, agrooved type, a conical type, and a flipper type, and combinationsthereof
 8. The temperature-compensated resonator according to claim 1,wherein the body is a Micro-Electro-Mechanical System.
 9. A timepiecethat includes at least one temperature-compensated resonator accordingto claim
 1. 10. A temperature-compensated resonator including a bodyused in deformation, wherein a core of the body is formed from a plateformed at a cut angle in a quartz crystal in order to determine firstand second orders temperature coefficients of the resonator that areboth negative, wherein the body includes a coating deposited at leastpartially on the core and having first and second orders Young's modulusvariations according to temperature that are respectively both positivein order to render the first and second orders temperature coefficientsof the resonator substantially zero.
 11. The temperature-compensatedresonator according to claim 10, wherein the body has a substantiallyquadrilateral-shaped section with faces in identical.
 12. Thetemperature-compensated resonator according to claim 10, wherein thebody includes a substantially quadrilateral-shaped section whose facesare entirely coated.
 13. The temperature-compensated resonator accordingto claim 10, wherein the body is a bar wound around itself to form abalance spring and is coupled with an inertia member.
 14. Thetemperature-compensated resonator according to claim 10, wherein thebody includes at least two symmetrically mounted arms forming a tuningfork.
 15. The temperature-compensated resonator according to claim 14,wherein the tuning fork is selected from the group consisting of aninverted type, a grooved type, a conical type, and a flipper type, andcombinations thereof.
 16. The temperature-compensated resonatoraccording to claim 10, wherein the body is a Micro-Electro-MechanicalSystem.
 17. A timepiece that includes at least onetemperature-compensated resonator according to claim
 10. 18. Thetemperature-compensated resonator according to claim 10, wherein thecoating includes germanium oxide.
 19. The temperature-compensatedresonator according to claim 10, wherein the coating includes tantalumoxide.